Order of play

In a recent Match Play comp round the following happened :
Player A's ball is on the green but far away from the hole, Player B's ball is on the fringe but nearer to the hole. Player B then proceeds to chip to "come onto" the green. Player A then tells Player B that he played out of turn and told Player B to replace the ball and replay the shot after Player A has putted.
What would be the ruling in this situation?

As far as I know there is no rule for stroke play. Speed of play, consideration of playing partners line, etc, are taken into account in stroke play. The rule exists in match play because there can be considerable advantage in going first

The rule does exist in stroke play (10-2b), but there is no penalty if it is not followed and the ball does not have to be replayed.
If, however, the Committee determines that competitors have agreed to play out of turn to give one of them an advantage, they are disqualified.

That would have to be the old "Paris in the the Spring" syndrome at work OB, as your brain rearranged the letters in the thread title.
My play is particularly odorous at times btw, but that's another story.
In match play I suppose you could always play out of turn on occasion and if you duff it you could tell your opponent that you need to replay the shot. Might just work.

Player Aâ€™s ball is on the green but far away from the hole, Player Bâ€™s ball is on the fringe but nearer to the hole. Player B then proceeds to chip to â€ścome ontoâ€ť the green. Player A then tells Player B that he played out of turn and told Player B to replace the ball and replay the shot after Player A has putted.

What would be the ruling in this situation?

Should Player A inform the player that he played out of turn before he actually putted himself? It seems a bit unfair for Player B to play out of turn but then not to be told so by Player A until after he had a putt?

Should Player A inform the player that he played out of turn before he actually putted himself? It seems a bit unfair for Player B to play out of turn but then not to be told so by Player A until after he had a putt?

Playing Out of Turn
If a player plays when his opponent should have played, there is no penalty, but the opponent may immediately require the player to cancel the stroke so made and, in correct order, play a ball as nearly as possible at the spot from which the original ball was last played

Player Aâ€™s ball is on the green but far away from the hole, Player Bâ€™s ball is on the fringe but nearer to the hole. Player B then proceeds to chip to â€ścome ontoâ€ť the green. Player A then tells Player B that he played out of turn and told Player B to replace the ball and replay the shot after Player A has putted.

What would be the ruling in this situation?

Should Player A inform the player that he played out of turn before he actually putted himself? It seems a bit unfair for Player B to play out of turn but then not to be told so by Player A until after he had a putt?